Poincaré inequalities in quasihyperbolic boundary condition domains
نویسندگان
چکیده
منابع مشابه
Poincaré Inequalities in Punctured Domains 1069
The classic Poincaré inequality bounds the Lq-norm of a function f in a bounded domain Ω ⊂ Rn in terms of some Lp-norm of its gradient in Ω. We generalize this in two ways: In the first generalization we remove a set Γ from Ω and concentrate our attention on Λ = Ω \ Γ. This new domain might not even be connected and hence no Poincaré inequality can generally hold for it, or if it does hold it m...
متن کاملQuasihyperbolic geodesics in convex domains
We show that quasihyperbolic geodesics exist in convex domains in reflexive Banach spaces and that quasihyperbolic geodesics are quasiconvex in the norm metric in convex domains in all normed spaces. 2000 Mathematics Subject Classification: 30C65
متن کاملWeak Poincaré Inequalities on Domains Defined by Brownian Rough Paths
where 0 ≤ s ≤ t ≤ 1 and ⊗ denotes a tensor product. Lyons [17] proved that solutions of stochastic differential equations (SDEs) are continuous functions of the Brownian rough path w(s, t) = ( w(s, t)1, w(s, t)2). We give a precise definition of the Brownian rough path in the next section; see also [18] and [15]. The discontinuity of solutions of SDEs in the uniform convergence topology of w ca...
متن کاملQuasihyperbolic geometry of domains in Hilbert spaces
The paper deals with basic smoothness and bilipschitz properties of geodesics, balls and spheres in the quasihyperbolic metric of a domain in a Hilbert space. 2000 Mathematics Subject Classification: 30C65
متن کاملOn Friedrichs – Poincaré - type inequalities ✩
Friedrichsand Poincaré-type inequalities are important and widely used in the area of partial differential equations and numerical analysis. Most of their proofs appearing in references are the argument of reduction to absurdity. In this paper, we give direct proofs of Friedrichs-type inequalities in H 1(Ω) and Poincaré-type inequalities in some subspaces of W1,p(Ω). The dependencies of the ine...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Manuscripta Mathematica
سال: 2015
ISSN: 0025-2611,1432-1785
DOI: 10.1007/s00229-015-0735-9